I would perceive this as "Microsoft invests in a minor competitor to Google" rather than "Microsoft invests in a Linux distribution."

As an Android user -- including having had about 5 years of that as a Cyanogenmod user and occasional ad hoc Cyanogenmod (and other Android) platform integrator -- I don't consider any of the various Android implementations to be "Linux distributions" as that term is understood.

Yes, they have Linux kernels, and they can use Linux kernel modules such as device drivers. From that point outward, however, they are operationally divergent. Android's process and resource management schema -- which applications must integrate with -- and the end user interfaces and resulting experience are completely different.